Question

Question)

Erika lives in a small town that is currently having a flu epidemic. Approximately 60% of the 5000 residents have the flu. If the flu test is 95% accurate (for both sensitivity and specificity), create a table to show the results if all 5000 residents are tested.

How many of the 5000 test results are true positive?

QUESTION)

Erika lives in a small town that is currently having a flu epidemic. Approximately 60% of the 5000 residents have the flu. If the flu test is 95% accurate (for both sensitivity and specificity), create a table to show the results if all 5000 residents are tested.

How many of the 5000 test results are true negative?

QUESTION )

Erika lives in a small town that is currently having a flu epidemic. Approximately 60% of the 5000 residents have the flu. If the flu test is 95% accurate (for both sensitivity and specificity), create a table to show the results if all 5000 residents are tested.

If Erika tests positive for having the flu, what is the probability she actually has the flu?

Leave your answer in decimal form and round it to 4 decimal places.

QUESTION)

Erika lives in a small town that is currently having a flu epidemic. Approximately 60% of the 5000 residents have the flu. If the flu test is 95% accurate (for both sensitivity and specificity), create a table to show the results if all 5000 residents are tested.

If Erika tests negative for having the flu, what is the probability that she does, in fact, have the flu?

Leave your answer in decimal form and round it to 4 decimal places.

Please, show me your all works. Thanks.

Answer 1

Erika's town is having a flu epidemic. And 60% of the population has the flu. So P(a person has flu) = 60/100=3/5

It is given that the accuracy of flu test is 95% (both specifcity and sensitivity)

So,

   (sensitivity)

and

(specifcity)

1. True positive is given by sensitivity so number of test results true positive = 5000 x (3/5) x 0.95 = 2850 (here 5000 x (3/5) gives the population that is actually positive)

2. True negative is given by specificity so number of test results true positive = 5000 x (2/5) x 0.95 = 1900 (here 5000 x (2/5) gives the population that is actually negative)

3. We have to find

b) By Bayes theorem,

By Law of total probability

P(tested positive) = P(tested positive | person is postive).P(person is positive) +

P( tested positive | person is negative).P(person is negative)   

= (0.95).(3/5) + (1 - P( tested negative | person is negative)).P(person is negative)   

= 0.57 + ( 1 - 0.95).(2/5) = 0.57 + 0.02 = 0.59

So,

4.

We have to find

b) By Bayes theorem,

By Law of total probability

P(tested negative) = P(tested negative | person is postive).P(person is positive) +

P( tested negative | person is negative).P(person is negative)   

= (1-0.95).(3/5) + (0.95).(2/5)

= 0.3 + 0.38 = 0.68

So,

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